#### Chapter 1 Elementary Arithmetic

Section 1.3 Transformation of terms

# 1.3.3 Exercises

##### Exercise 1.3.9
Simplify the following terms for appropriate numbers $a$, $b$, $x$, $y$, $z$:
1. $\frac{3x-6x{y}^{2}+4xyz}{-2x}$$=$
.
2. $\left(3a-2b\right)·\left(4a-6\right)$$=$
.
3. $\left(2a+3b{\right)}^{2}-\left(3a-2b{\right)}^{2}$$=$
.
4. $\frac{3a}{3a+6b}+\frac{2b}{a+2b}$$=$
.
The input must not contain any brackets.

##### Exercise 1.3.10
For the following exercises a little more patience is required. Simplify:
1. $\frac{1}{2}x\left(4x+3y\right)+\frac{3}{2}\left(5{x}^{2}-6xy\right)$$=$
.
2. $\frac{18{x}^{2}-48xy+32{y}^{2}}{12y-9x}·\frac{18x+24y}{9{x}^{2}-16{y}^{2}}$$=$
.
3. $\left({a}^{2}+5a-2\right)\left(2{a}^{2}-3a-9\right)-\left(\frac{1}{2}{a}^{2}+3a-5\right)\left({a}^{2}-4a+3\right)$$=$
.
The input must not contain any brackets.

##### Exercise 1.3.11
Use a binomial formula to calculate the following squares:
1. ${43}^{2}$$=$
.
2. ${97}^{2}$$=$
.
3. ${41}^{2}-{38}^{2}$$=$
.

##### Exercise 1.3.12
Apply a binomial formula to expand the product and collect like terms:
1. $\left(-5xy-2{\right)}^{2}$$=$
.
2. $\left(-6ab+7bc\right)\left(-6ab-7bc\right)$$=$
.
3. $\left(-6ab+7bc\right)\left(-6ab+7bc\right)$$=$
.
4. $\left({x}^{2}+3\right)\left(-{x}^{2}-3\right)$$=$
.
The input must not contain any brackets.
##### Exercise 1.3.13
Factorise the following terms as far as possible using one of the binomial formulas:
1. $4{x}^{2}+12xy+9{y}^{2}$$=$
.
2. $64{a}^{2}-96a+36$$=$
.
3. $25{x}^{2}-16{y}^{2}+15x+12y$$=$
.
Factorise the result until it fits into the input field.